This month's topics:

"The Man Who Knew Infinity"

a film telling the story of Srinivasa Ramanujan, opens in the U.S. on April 29, 2016. On April 20 the New York Times ran "A Math Biopic, With Dev Patel, Applies a Different Calculus," by Kathryn Shattuck, giving us background information and describing some of the problems that arose in bringing the story to the screen.

For an understanding of Ramanujan, Shattuck spoke with the mathematician Ken Ono, who was a consultant on the film: "In a way, he was some kind of prophet. Whatever inspired him to write down his formulas was magic, because they're precisely the things that we've discovered would be needed long after his death." His importance resides in "the implications of his work that we are still beginning to only see glimpses of today. It's like he was writing down a bible for us, but it was incomplete. He gave us glimpses of what the future would be, and our job is to figure it out."

She also spoke with the stars of the film.

Jeremy Irons (G. H. Hardy): "It's about mathematics intrinsically, and I don't think your run-of-the-mill audience is attracted by mathematics. But what it turns out to be is the story of an extraordinary relationship with math as a background and a shared passion." (as Shattuck interpolates, "a passion so evident when he read Mr. Hardy's essay A Mathematician's Apology that it initially overwhelmed him.") "The world of the unknown was waiting, and it was up to a great mathematician to discover it."

Dev Patel (Ramanujan); she reports that Patel wanted to imbue his Ramanujan with "an essence of nobility, despite his humble beginnings. He was a reserved man but incredibly enlightened as a human being." Patel also tells us how he learned how to write an especially complicated equation on the blackboard. "They thought they were going to have to use some sort of trickery. But I bashed it out ... It felt quite satisfying."

Who needs Math? (Cont.)

Andrew Hacker's book The Math Myth: And Other STEM Delusions, where he gives a complete presentation of the theses sketched in his various interviews and op-ed columns (previously mentioned here and here), was reviewed on March 29, 2016 by Evelyn Lamb in the online magazine Slate. The headline: "It Doesn't Add Up"; the subhead reads: "Andrew Hacker argues that abstract math is scary, damaging, and should be optional in American education. He should check his calculations."

Lamb begins by summarizing Hacker's main points: that too many students drop out because they fail math classes, and that the solution is to replace the current math curriculum by courses emphasizing numeracy ("a facility with numbers and arithmetic as they generally show up in everyday life") and "citizen statistics" ("an ability to understand and contextualize figures that appear in media and politics"). She goes on to agree that "Hacker's conclusions are not entirely without merit." She has reservations, but her main objection (buttressed by many examples) is that Hacker's arguments are mendacious, and that many of his examples are mathematically wrong. "Over and over again, he relies on the reader's ignorance or fear of mathematics to make mathematics education sound scarier than it is. These repeated misunderstandings and misrepresentations undermine his credibility. I know much more about math than I do about pedagogy, policy, and other topics he addresses. If a huge amount of what he says about math is incorrect or misleading, why should I trust him on the other subjects?" Her conclusion: "Of course we should work to make mathematics education better. But while we consider the options, we shouldn't let our emotional reactions to math terminology lead us to accept shoddy arguments from Hacker or anyone else."

[One aspect of Hacker's critique of secondary and college mathematics education that most observers seem to have overlooked is his stated opinion that the sad state of affairs is largely due to interference from the theoretical-math establishment. This appears in his interviews and op-ed pieces, but most prominently in his essay "The Math Mandarins" (Chronicle of Higher Education, March 20, 2016). To summarize a long argument in a few words: mathematics education is directed from afar by a small (200 people?) elite group of senior professors at top-tier universities. In order to perpetuate their kind they have forced an entire nation to undergo the basic training for their profession. And it's not working, largely because they themselves, and their acolytes, are too busy with their absurdly esoteric research to waste their talents on demeaning activities like teaching. -TP]

Mathematics: a young man's game?

That it is was famously proclaimed by G. H. Hardy in A Mathematician's Apology, the very book that overwhelmed Jeremy Irons in this month's first item. Manil Suri, mathematician and novelist, has a New York Times opinion piece "The Mathematician's 90th-Birthday Party" where he presents Ivo Babuska (University of Texas, Austin) as a counterexample. As the title suggests, Suri recently attended a conference celebating Babuska's 90th birthday; he reports: "Ivo remains passionately immersed in research, despite the dearly held popular belief that mathematicians are over the hill at 40."

Suri makes the point that if one considers mathematics a game, where originality and elegance are the most important criteria, then indeed youth can be an advantage. He quotes John Tate [an algebraist] as stating that mathematicians do their best work when they "don't have a lot of baggage" and "haven't worn grooves in their brains." But there is more to mathematics. As Suri tells us, "Ever since its inception, mathematics has also been driven by another powerful force: applications. From the early commerce and measurement needs that motivated the Sumerians to the subject's symbiotic co-development with physics, mathematical inquiry has been spurred by questions from external fields." And here is where "experience and maturity help." "Ivo's most profusely cited paper, published when he was 70, contains one of those clarifying, deceptively simple-looking ideas that can emerge only with the deep and broad insight of a long career: a general mathematical method that can be (and is being!) used by engineers to design better machine parts."

Babuska has doctorates in both engineering and mathematics. "In this, he embodies another skill enhanced by experience -- the ability to interact with non-mathematicians, to interpret their questions mathematically and to explain solutions in their language. Hardy dismissed exposition as 'work for second-rate minds,' but such activity is critical for a field notoriously inept at communicating its results to outsiders." Finally: "Let's cherish Hardy's theorems, not his opinions, and recognize mathematics as a field with diverse goals and needs, where people can expect to make useful contributions regardless of gender or age."

"The Great Math Mystery," redux on NOVA

On March 30, 2016 PBS rebroadcast their sumptuous exploration of the relation between mathematics and reality, and in particular the question, going back to Eugene Wigner, of the "unreasonable effectiveness" of mathematics in describing and explaining physical phenomena. The program ends with a typically troubling spoken contribution from Stephen Wolfram: "I think it's an illusion, because I think what's happened is that people have chosen to build physics, for example, using the mathematics that has been practiced, has developed historically, and they're looking at everything, they're choosing to study things which are amenable to study using the mathematics that happens to have arisen; but actually there is a whole vast ocean of other things that are really quite inaccessible to these methods."